Hobill, David WesleyRaghoonundun, Ambrish Mangeshwar2016-04-252016-04-2520162016http://hdl.handle.net/11023/2897Seven new solutions to the interior static and spherically symmetric Einstein’s field equations (EFE) are found and investigated. These new solutions are a generalisation of the quadratic density fall-off profile of the Tolman VII solution. The generalisation involves the addition of anisotropic pressures and electric charge to the density profile. Of these new solutions three are found to obey all the necessary conditions of physical acceptability, including linear stability under radial perturbations, and causality of the speed of pressure waves inside the object. Additionally an equation of state can be found for all the physically viable solutions. The generalised pulsation equation for interior solutions to the EFE that include both electric charge and pressure anisotropy is derived and used to determine the stability of the solutions. However the pulsation equation found is general and can be used for all new solutions that contain these ingredients.engUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.PhysicsAstronomy and AstrophysicsExact solutionsEinstein's equationsCompact Objectsdoctoral thesis10.11575/PRISM/26010